C> @file

C> @brief Perform a scalar spherical transform.

C>

C> ### Program History Log

C> Date | Programmer | Comments

C> -----|------------|---------

C> 96-02-29 | IREDELL | Initial

C> 1998-12-15 | IREDELL | Generic fft used, openmp directives inserted

C>

C> @author IREDELL @date 96-02-29

C> This subprogram performs a spherical transform between spectral

C> coefficients of scalar quantities and fields on a global

C> cylindrical grid.

C>

C> The wave-space can be either triangular or

C> rhomboidal.

C>

C> The grid-space can be either an equally-spaced grid

C> (with or without pole points) or a Gaussian grid.

C>

C> The wave and grid fields may have general indexing,

C> but each wave field is in sequential 'IBM order',

C> i.e. with zonal wavenumber as the slower index.

C>

C> Transforms are done in latitude pairs for efficiency;

C> thus grid arrays for each hemisphere must be passed.

C> If so requested, just a subset of the latitude pairs

C> may be transformed in each invocation of the subprogram.

C>

C> The transforms are all multiprocessed over latitude except

C> the transform from Fourier to spectral is multiprocessed

C> over zonal wavenumber to ensure reproducibility.

C>

C> Transform several fields at a time to improve vectorization.

C> Subprogram can be called from a multiprocessing environment.

C>

C> Minimum grid dimensions for unaliased transforms to spectral:

C> DIMENSION |LINEAR |QUADRATIC

C> ----------------------- |--------- |-------------

C> IMAX | 2*MAXWV+2 | 3*MAXWV/2*2+2

C> JMAX (IDRT=4,IROMB=0) | 1*MAXWV+1 | 3*MAXWV/2+1

C> JMAX (IDRT=4,IROMB=1) | 2*MAXWV+1 | 5*MAXWV/2+1

C> JMAX (IDRT=0,IROMB=0) | 2*MAXWV+3 | 3*MAXWV/2*2+3

C> JMAX (IDRT=0,IROMB=1) | 4*MAXWV+3 | 5*MAXWV/2*2+3

C> JMAX (IDRT=256,IROMB=0) | 2*MAXWV+1 | 3*MAXWV/2*2+1

C> JMAX (IDRT=256,IROMB=1) | 4*MAXWV+1 | 5*MAXWV/2*2+1

C>

C> @param IROMB spectral domain shape

c> (0 for triangular, 1 for rhomboidal)

C> @param MAXWV spectral truncation

C> @param IDRT grid identifier

C> - IDRT=4 for Gaussian grid,

C> - IDRT=0 for equally-spaced grid including poles,

C> - IDRT=256 for equally-spaced grid excluding poles

C> @param IMAX even number of longitudes.

C> @param JMAX number of latitudes.

C> @param KMAX number of fields to transform.

C> @param IPRIME longitude index for the prime meridian.

C> (defaults to 1 if IPRIME=0)

C> @param ISKIP skip number between longitudes

C> (defaults to 1 if ISKIP=0)

C> @param JNSKIP skip number between n.h. latitudes from north

C> (defaults to imax if JNSKIP=0)

C> @param JSSKIP skip number between s.h. latitudes from south

c> (defaults to -imax if JSSKIP=0)

C> @param KWSKIP skip number between wave fields

c> (defaults to (MAXWV+1)*((IROMB+1)*MAXWV+2) IF KWSKIP=0)

C> @param KGSKIP skip number between grid fields

c> (defaults to IMAX*JMAX IF KGSKIP=0)

C> @param JBEG latitude index (from pole) to begin transform

c> (defaults to 1 if JBEG=0)

C> (if JBEG=0 and IDIR<0, wave is zeroed before transform)

C> @param JEND latitude index (from pole) to end transform

c> (defaults to (JMAX+1)/2 IF JEND=0)

C> @param JCPU number of cpus over which to multiprocess

C> @param[out] WAVE wave fields if IDIR>0

C> @param[out] gridn n.h. grid fields (starting at jbeg) if IDIR<0

C> @param[out] grids s.h. grid fields (starting at jbeg) if IDIR<0

C> @param IDIR transform flag

C> (idir>0 for wave to grid, idir<0 for grid to wave)

C>

C> @author IREDELL @date 96-02-29

SUBROUTINE SPTRAN(IROMB,MAXWV,IDRT,IMAX,JMAX,KMAX,

& IPRIME,ISKIP,JNSKIP,JSSKIP,KWSKIP,KGSKIP,

& JBEG,JEND,JCPU,

& WAVE,GRIDN,GRIDS,IDIR)

REAL WAVE(*),GRIDN(*),GRIDS(*)

MX=(MAXWV+1)*((IROMB+1)*MAXWV+2)/2

IP=IPRIME

IS=ISKIP

JN=JNSKIP

JS=JSSKIP

KW=KWSKIP

KG=KGSKIP

JB=JBEG

JE=JEND

JC=JCPU

IF(IP.EQ.0) IP=1

IF(IS.EQ.0) IS=1

IF(JN.EQ.0) JN=IMAX

IF(JS.EQ.0) JS=-JN

IF(KW.EQ.0) KW=2*MX

IF(KG.EQ.0) KG=IMAX*JMAX

IF(JB.EQ.0) JB=1

IF(JE.EQ.0) JE=(JMAX+1)/2

IF(JC.EQ.0) JC=NCPUS()

IF(IDIR.LT.0.AND.JBEG.EQ.0) THEN

DO K=1,KMAX

KWS=(K-1)*KW

WAVE(KWS+1:KWS+2*MX)=0

ENDDO

ENDIF

CALL SPTRANF(IROMB,MAXWV,IDRT,IMAX,JMAX,KMAX,

& IP,IS,JN,JS,KW,KG,JB,JE,JC,

& WAVE,GRIDN,GRIDS,IDIR)

END